Non literal tranducers and some problems of normality

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Abstract

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A new proof of Maxfield’s theorem is given, using automata and results from Symbolic Dynamics. These techniques permit to prove that points that are near normality to base pk (resp. p) are also near normality to base p (resp. pk), and to study genericity preservation for non Lebesgue measures when going from one base to the other. Finally, similar results are proved to bases the golden mean and its square.